Name: __________________________________________ Date: _____________________ Per: ____
Geometry Semester 1 Final Exam Review
Chapter 1: Tools of Geometry
1) Find a pattern for the sequence. Use the pattern to show the next three terms. 15, 12, 9, 6, …
2) If two lines intersect, then they intersect in a ___________________.
3) If two planes intersect, then they intersect in a __________________.
4) Which of the following could not be the intersection of two planes?
a. AB b. BA c. B d. ABC e. point A
5) B is the midpoint of AC . If 2 1AB x and 3 4BC x , what is x? What is the measure of BC ? What is
the measure of AC ?
6) Find the midpoint and distance on a number line between 6 and -15.
7) S is between R and T. If 64, 3 1RT RS x and 2 2ST x , find x.
8) Draw an example of each of the following
a. Complementary b. Supplementary c. Vertical angles d. Adjacent
Angles angles angles
9) 2 8, 3 14, 7 2m RST x m TSW x m RSW x . Find m TSW .
10) Find .m RQS
2 4x 6 20x
T Q R
S
11) Find the measure of x.
3 31x 2 6x
12) Find TO given
2 12
5
50
TO x
OP x
TP
13) What is the measure of this angle?
How would you classify the angle?
14) EM bisects GEO
3 5
29
m GEM x
m MEO x
Find m GEO .
15) 2 15m GIT x
4 5
m FIT x
m GIF x
Find m GIT .
16) Given the points 2, 4 and 5,1 :
a. Find the distance between the points.
b. Find the midpoint between the points.
17) Given the points 6, 5 and 3,2 :
a. Find the distance between the points to the nearest tenth.
b. Find the midpoint between the points.
18) O is the midpoint of DG . Find the coordinate of G if O is 7 and D is 3.
T O P
G
T I
F
19) Which is the missing endpoint if the midpoint is 0, 6 and the other endpoint is 3,8 ?
a. (1.5, 1) b. (1, 1.5) c. (-3, -20) d. (20,-3)
20) I. What is the circumference of a circle with: (Leave answers in form)
a. Radius of 4 cm b. diameter of 32 cm
II. What is the area of a circle with: (Leave answers in form)
b. Radius of 4 cm b. diameter of 32 cm
21) The perimeter of a rectangle is 28 feet and the base is 8 feet. What is the height?
22) The area of a rectangle is 254 cm and the height is 9 cm. What is the base?
Chapter 2: Reasoning and Proof
23) Given the sentence “If you are good, then Santa will bring you presents,” write:
a. The converse:
b. The inverse:
c. The contrapositive:
d. The biconditional:
24) Draw a conclusion:
-If a student gets an A on the final exam, then the student will pass the course.
-Felicia gets an A on the music theory final exam.
25) Draw a conclusion:
-If it is a national holiday, then school is not in session.
-If school is not in session, then students are at home.
26) Which property of equality or congruence justifies each statement?
a. If 3 14 80x , then 3 66x .
b. If 15m A , then 3 45m A .
c. If 4 100m C , then 25m C .
27) Solve for y.
28) Solve for x.
29) ABC and DBC are complementary. What is the m DBC if 4 10m ABC x and 30m DBC x ?
30) If the supplement of T is 47 , what is the measure of T ?
Chapter 3: Parallel and Perpendicular Lines
31) Determine the relationship of the following angles.
a. 1 and 2
b. 1 and 6
c. 3 and 6
d. 1 and 7
e. 1 and 5
f. 2 and 4
32) Fill in the blank.
a. Angles that form a linear pair ___________________________.
b. Angles that are vertical are _____________________________.
c. Corresponding angles of parallel lines are _______________________________.
d. Same-side interior angles of parallel lines are ______________________________.
4 3 2 1
5 6
7 8
e. Alternate interior angles of parallel lines are _______________________________.
33) If 50, 130, 50m A m B m C , and they fall on parallel lines cut by a transversal
a. Which angles could be vertical?
b. Which angles could be same-side interior?
c. Which angles could be alternate interior?
34) In FUN , the angles measure 3 , 2 20 , 5 5x x and x , what is the measure of the smallest angle?
35) What is ?m DBA
36) What is the value of x?
37) What is the value of x?
38) If 60m A and 60m B , ABC is what kind of triangle? Classify by angles and sides.
39) If 45m A and 45m B , ABC is what kind of triangle? Classify by angles and sides.
40) Classify the triangle according to the angle and side length.
B C A
D
x
x 63
36
41) Find the missing angle measure.
a. b.
42) Find the sum of the measures of each polygon.
a. Dodecagon b. nonagon
43) Find the measure of an interior angle and an exterior angle of each regular polygon.
a. Pentagon b. 18-gon
44) Find the slope of the line passing through the following points:
a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)
45) Find the slope of the line parallel to the line passing through the following points:
a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)
46) Find the slope of the line perpendicular to the line passing through the following points:
a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)
47) Determine which line is perpendicular to 2
63
y x .
a. 2
73
y x
b. 3
52
y x c. 3
82
y x
d. 2
63
y x
48) Determine which line is parallel to 4 3y x .
a. 1
74
y x
b. 1
54
y x c. 4 8y x d. 4 6y x
49) How can you determine if two lines are parallel?
50) How can you determine if two lines are perpendicular?
51) How can you determine if two lines intersect, but are not perpendicular?
52) Given AD BC , find m BDA
53) Given: l m , find x.
Chapter 4: Congruent Triangles
54) Given that IMP OGR , name all of the pairs of corresponding parts.
55) For each figure below, state the parts you would need to know are congruent in order to prove the triangles
congruent by the method stated.
a. SAS b. AAS
C T
c. HL d. ASA
56) Use the given information to make a conclusion about each figure.
a. I) Y is the midpoint of RD
II) UY RD
A B
C D
B
T
I
D
M A
M T
S
R
D U
P M
D
C
A
T
O
G
R
U
Y D
III) UY bisects RUD
b.
I) DA QU
II) What parts are congruent just by the picture?
57) Given: JOA ADJ
ON ND
Prove: JON ADN
58) Given: T is the midpoint of GF
GTI FTI
Prove: G F
59) Given: SL CL
SA AU
SC SU
SLA is isosceles with base LA
Prove: SCL SUA
J
O N
A
D
R
I
G F T
D A
Q U
S U
A
L C
60) A is the midpoint of LU
2 14
3 24
10
CAL x
SAU x
CA x
Find the measure of SA .
61) Find x
62) TAP is isosceles with vertex angle t.
Find m A .
63) DAN is isosceles with base AD .
4 12
33
A x
D x
Find m D
64) ABC is isosceles with A as the vertex angle. If 3 4, 5 8m B x m C x . Find m B
Chapter 5: Relationships within Triangles
C
L A
S
U
x
P
T
A
D A
N
65) In ,MLK MK is 20in. long. What is its midsegment?
66) Solve for x.
67) Solve for y.
68) a. If 24, 6, 8DF BC and DB ,
what is the perimeter of EBC ?
b. If the perimeter of BCE is 17,
what is the perimeter of ADF ?
69) LJ bisects KLM , find x, JK, and JM.
70) AB is a median. CD = 18, BD = x-6. Solve for x.
84
D
B C
A E F
J
K
L M
B
A
D C
71) G is the centroid
a. If GD = 7, what is AG?
b. If GC = 12, what is CF?
c. If EB = 48, what is GB?
72) In , 10 , 16 , 14FUN UN cm UF cm and FN cm . Which angle is the smallest?
73) In , 47, 93HAT A T . List the sides in order from least to greatest.
74) Could the following be lengths of a triangle?
a. 5, 9, 13
b. 7, 14, 20
c. 1, 5, 7
d. 2, 2, 3
75) If one side of a triangle is 17 cm and the second side is 39 cm, what are the possible side lengths for the third
side?
Geometry Semester II Review Packet #1
A
E
C
D F
B
G
8.1 Ratio and Proportion Ratio = Proportion = Solve proportions by cross multiplying. extremes means
a c
b d
word problems – set up what is being compared
8.1
1. 3 9
4 12 Name the means.
2. Is 7
8
x
y equivalent to
7
8
x
y?
3. Solve. 11
5 35
x
4. Solve.
2 5
8
x
x
5. The angles of a triangle are in the ratios
3:5:7. Find each angle measure.
6. If 2 CDs cost $14.50, how much will 15
CDs cost?
7. A 15 foot building has a 9 foot shadow.
How tall is a building with a 30 foot
shadow?
8.2 Similar Polygons Similar polygons:
1) Corresponding angles are congruent. 2) Corresponding sides have equal ratios.
Scale factor = ratio of sides
8.2
8. What is the scale factor of ABCD to
EFGH?
9. Find EF, FG, and GH.
10. Find x and y.
D
A
C
B
12
25
8
20
E F
G
H
6
ABCD ~ EFGH
18 30
24
20
x
y
8.3 Similar Triangles Ways to prove similar triangles:
1) SSS~ 2) SAS~ 3) AA~
8.3
11. Are these triangles similar? Why?
12. Are these triangles similar? Why?
13. ABC DEF
15
20
25
16
AB
AC
BC
DF
8.4 Proportional Parts Side-splitter
a c
b d
Midsegment:
1) ½ the 3rd side 2) Parallel to the 3rd side
a c
b d
8.4
14. Find x and y.
15. Find x.
16. Find x and y.
12
8
9
6
Find EF
Find DE
15
24
y
10
x
52
4
x
a
b d
c
a
b d
c
2
3 x
8
5 y
8.5 Parts of Similar Triangles In similar triangles, the ratio of the sides is also the ratio of the:
Perimeters
Medians
Altitudes
Angle bisectors
8.5
17. Find x and perimeter.
~
18. Find x.
8 10
P = 28
6 x
P = ?
9 6
x 8
Answers:
1) 3, 0, -3
2) Point
3) Line
4) C, D, E
5) X = 5, 11, 22BC AC
6) Midpoint: -4.5, Distance: 21
7) X = 13
8) A)
B)
C)
D)
9) X = 12, 50m TSW
10) X = 19.5, 137m RQS
11) X = 31
12) X = 11, 34TO
13)
14) X = 12, 82m GEO
15) X = 10, 35m GIT
16) A) 74 8.60
B) 3 3
,2 2
17) A) 130 11.4
B) 3 3
,2 2
18) 11
19) C
20) IA) 8 cm IB) 32 cm
IIA) 216 cm IIB) 2256 cm
21) h = 6 ft
22) b = 6 cm
23) a) If Santa brings you presents, then you
were good
b) If you are not good, then Santa will
not bring you presents
c) If Santa does not bring you presents,
then you were not good
d) Santa will bring you presents if and
only if you are good
24) Felicia will pass the course
25) If it is a national holiday, then students are
at home
26) a) Subtraction property of equality
b) Multiplication property of equality
c) Division property of equality
d) Symmetric property of congruence
27) y = 18
28) x = 6
1 2
29) x = 14, 44m DBC
30) 133m T
31) a) Supplementary angles
b) Alternate interior angles
c) Corresponding angles
d) Corresponding angles
e) Same-side interior angles
f) Vertical angles
32) a) are supplementary
b) Congruent
c) Congruent
d) Supplementary
e) Congruent
33) a) ,A C
b) , , ,A B and C B
c) ,A C
34) x = 15,5, smallest angle = 46.5
35) 110m DBA
36) 70x
37) x = 50
38) Equiangular and equilateral
39) Right and isosceles
40) Acute and scalene
41) a) 102y
b) n = 113, n+6=119
42) a) 1800 b) 1260
43) a) interior = 108, exterior = 72
b) interior = 160, exterior = 20
44) a) m = 2 b) 17
9m
45) a) m = 2 b) 17
9m
46) a) 1
2m
b)
9
17m
47) C
48) D
49) If the slopes are the same
50) If the slope are opposite reciprocals
51) The slopes are different by not opposite
reciprocals
52) 40m BDA
53) x = 20
54) , ,I O M G P R
, ,IM OG MP GR IP OR
55) A) BI MD
B) T G
C) RM RS
D) MUP DPU
56) AI) RY YD
AII) 90m UYD m UYR
AIII) RUY DUY
BI) DAQ UQA
BII) QA QA reflexive property
57) Statement Reason
JOA ADJ Given
ON ND Given
ONJ DNA Vertical angles
JON ADN ASA
58) Statement Reason
T is the midpoint of GF Given
GTI FTI Given
TI TI Reflexive
GTI FTI SAS
G F CPCTC
59) Statement Reason
SL CL Given
SA AU Given
SC SU Given
SLA is isosceles Given
CLS and UAS Definition perpendicular
are right angles lines
CLS UAS All rt. Angles are
congruent
SCL SUA HL
60) x = 38, SA = 28
61) x – 80
62) 62.5m A
63) x = 15, 48m D
64) x = 6, 22m B
65) 10 in
66) x = 23
67) y = 7
68) a) 52 units b) 34 units
69) x = 12, JK = 17, JM = 17
70) x = 15
71) a) 14 b) 18 c) 16
72) F
73) , ,AT HT AH
74) a) yes b) yes
c) no d) yes
75) 22 56x
8.1
1) 4 & 9
2) 3 & 12
3) no
4) 16/3
5) 12
6) 108.75
7) 50 ft
8) 4:3
9) EF =15
FG = 9
GH = 75/4
10) x = 16, y=12
8.3
11) yes, SAS~
12) yes, AA